Well, Einstein says the definition of insanity is doing the same thing over and over again and expecting different results, and as such, I predeclare that I'm insane. I had already set those port numbers and authentications on my server settings tab, but I retyped my password (just as I had several times before), and dutifully (i.e. insanely) tried it again. And whallah... It worked.
I can't imagine I had mistyped my password so often previously to keep it from working, but apart from that I don't know what's different about this time than the time before.
But for anyone else who comes across this thread from a search result, with similar issues, he are the settings that worked for me....
incoming server name: pop.secureserver.net
Port number: 995 Check Secure connection (TLS)
Authentication: Auto (Plaintext) -- although Plaintext should work just as well
Username: firstname.lastname@example.org (make sure it has the @-sign and the full domain name)
Outgoing server: smtpout.secureserver.net
Port number: 465 Check Secure connection (TLS)
Username: email@example.com (same username as for the incoming server)